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To round a decimal to a specified place value, follow four steps:

1. **Locate** the digit in the target place value and mark it.
2. **Examine** the digit immediately to the right of the target place.
3. **Decide** — if that digit is $$5$$ or greater, add $$1$$ to the digit in the target place; if it is less than $$5$$, leave the target-place digit unchanged.
4. **Rewrite** the number, deleting all digits to the right of the target place.

This procedure mirrors the one used for rounding whole numbers, with one key difference in the final step: instead of replacing digits to the right with zeros (as with whole numbers), those digits are simply removed. Trailing zeros after the last nonzero decimal digit do not change a decimal's value, so they are unnecessary in the rounded result.

Procedure for Rounding Decimals

To round $$18.379$$ to the nearest hundredth, apply the four-step decimal rounding procedure:

1. **Locate the hundredths digit:** In $$18.379$$, the digit in the hundredths place is $$7$$.
2. **Look at the next digit:** The digit immediately to the right of $$7$$ is $$9$$.
3. **Compare with $$5$$:** Because $$9 \geq 5$$, add $$1$$ to the hundredths digit, changing $$7$$ to $$8$$.
4. **Remove trailing digits:** Delete the $$9$$ (and any digits that would follow it).

The rounded result is $$18.38$$.

Rounding 18.379 to the Nearest Hundredth

To round $$18.379$$ to the nearest tenth, apply the four-step decimal rounding procedure:

1. **Locate the tenths digit:** In $$18.379$$, the digit in the tenths place is $$3$$.
2. **Look at the next digit:** The digit immediately to the right of $$3$$ is $$7$$.
3. **Compare with $$5$$:** Because $$7 \geq 5$$, add $$1$$ to the tenths digit, changing $$3$$ to $$4$$.
4. **Remove trailing digits:** Delete the $$7$$ and $$9$$ (all digits to the right of the tenths place).

The rounded result is $$18.4$$. Notice that the deleted digits are **not** replaced with zeros — they are simply dropped, since trailing zeros after a decimal's last nonzero digit do not change its value.

Rounding 18.379 to the Nearest Tenth

To round $$18.379$$ to the nearest whole number, apply the four-step decimal rounding procedure:

1. **Locate the ones digit:** In $$18.379$$, the digit in the ones place is $$8$$.
2. **Look at the next digit:** The digit immediately to the right of $$8$$ is $$3$$.
3. **Compare with $$5$$:** Because $$3 < 5$$, leave the ones digit unchanged at $$8$$.
4. **Remove trailing digits:** Delete the $$3$$, $$7$$, and $$9$$ (the entire decimal portion).

The rounded result is $$18$$. This example illustrates the round-down case: when the digit to the right of the target place is less than $$5$$, the target digit stays the same and all digits to its right are removed.

Rounding 18.379 to the Nearest Whole Number

Divide $$\$3.99 \div 24$$ by applying the decimal division procedure and rounding the result to the nearest cent:

1. **Set up the division:** The divisor $$24$$ is already a whole number, so no decimal-point shifting is needed. Place the decimal point in the quotient directly above the decimal point in the dividend $$3.99$$.
2. **Extend the dividend:** Because the answer involves money, it must be rounded to the nearest cent — the hundredths place. To round correctly, the division must be carried out to the thousandths place. Append a zero to the dividend, making it $$3.990$$.
3. **Perform long division:**
   - $$24$$ into $$39$$: $$1$$ time ($$24$$), remainder $$15$$.
   - Bring down $$9$$: $$24$$ into $$159$$: $$6$$ times ($$144$$), remainder $$15$$.
   - Bring down $$0$$: $$24$$ into $$150$$: $$6$$ times ($$144$$), remainder $$6$$.
   The quotient so far is $$0.166$$.
4. **Round to the nearest cent:** The hundredths digit is $$6$$ and the thousandths digit is also $$6$$. Since $$6 \geq 5$$, round up: $$\$0.166 \approx \$0.17$$.

Therefore, $$\$3.99 \div 24 \approx \$0.17$$. This example illustrates a key rule for money problems: always carry the division one place beyond the rounding target (to the thousandths place when rounding to the nearest cent) so that the rounding digit can be correctly determined.

Dividing \$3.99 ÷ 24

Round $$\sqrt{17}$$ to two decimal places by using a calculator and then applying the decimal rounding procedure.

**Step 1 — Use the calculator square root key.** Enter $$17$$ and press the $$\sqrt{x}$$ key to obtain the display value: $$4.123105626\ldots$$

**Step 2 — Round to two decimal places.** The hundredths digit is $$2$$, and the digit to its right is $$3$$. Since $$3 < 5$$, the hundredths digit stays at $$2$$. Drop all digits after the hundredths place.

**Result:** $$\sqrt{17} \approx 4.12$$

The approximation symbol $$\approx$$ is used because $$4.12$$ is a rounded value, not the exact square root of $$17$$.

Rounding $$\sqrt{17}$$ to Two Decimal Places

A logistics coordinator needs to round a shipping weight to the nearest tenth for a manifest. Arrange the standard steps for rounding a decimal number in the correct order.

A medical assistant is rounding a patient's weight in kilograms for an electronic health record. After the assistant has determined whether to increase the digit in the target place value based on the digit to its right, what is the correct final step in the standard procedure for rounding decimals?

A payroll specialist is rounding an employee's hourly wage to the nearest cent. According to the standard procedure for rounding decimals, the final step is to replace all digits to the right of the target place with zeros.

An auditor is rounding financial figures for a year-end report. Match each step of the standard decimal rounding procedure with its correct description.

A quality control inspector is rounding a product's precise weight to the nearest hundredth for a compliance report. According to the standard procedure for rounding decimals, state the specific rule used to decide whether to add 1 to the digit in the target place or leave it unchanged.

Decimal Rounding: Decision Criteria

A quality control technician is rounding a precise measurement for a compliance report. According to the standard four-step procedure for rounding decimals, after the digit in the target place has been adjusted, the final step is to ____ all digits to the right of that target place value.

Based on the standard procedure for rounding decimals, list the four specific steps you should include in the 'Rounding Protocol' to guide pharmacy staff on how to round a decimal number correctly.

Establishing Standard Operating Procedures for Pharmacy Dosages

To round $$6.582$$ to the nearest hundredth, apply the four-step decimal rounding procedure:

1. Locate the hundredths digit: In $$6.582$$, the digit in the hundredths place is $$8$$.
2. Look at the next digit: The digit immediately to the right of $$8$$ is $$2$$.
3. Compare with $$5$$: Because $$2 < 5$$, leave the hundredths digit unchanged at $$8$$.
4. Remove trailing digits: Delete the $$2$$ (all digits to the right of the hundredths place).

The rounded result is $$6.58$$.

Rounding 6.582 to the Nearest Hundredth

To round $$6.582$$ to the nearest tenth, apply the four-step decimal rounding procedure:

1. Locate the tenths digit: In $$6.582$$, the digit in the tenths place is $$5$$.
2. Look at the next digit: The digit immediately to the right of $$5$$ is $$8$$.
3. Compare with $$5$$: Because $$8 \geq 5$$, add $$1$$ to the tenths digit, changing $$5$$ to $$6$$.
4. Remove trailing digits: Delete the $$8$$ and $$2$$ (all digits to the right of the tenths place).

The rounded result is $$6.6$$.

Rounding 6.582 to the Nearest Tenth

To round $$6.582$$ to the nearest whole number, apply the four-step decimal rounding procedure:

1. Locate the ones digit: In $$6.582$$, the digit in the ones place is $$6$$.
2. Look at the next digit: The digit immediately to the right of $$6$$ is $$5$$.
3. Compare with $$5$$: Because $$5 \geq 5$$, add $$1$$ to the ones digit, changing $$6$$ to $$7$$.
4. Remove trailing digits: Delete the $$5$$, $$8$$, and $$2$$ (the entire decimal portion).

The rounded result is $$7$$.

Rounding 6.582 to the Nearest Whole Number

To round $$15.2175$$ to the nearest thousandth, apply the four-step decimal rounding procedure:

1. Locate the thousandths digit: In $$15.2175$$, the digit in the thousandths place is $$7$$.
2. Look at the next digit: The digit immediately to the right of $$7$$ is $$5$$.
3. Compare with $$5$$: Because $$5 \geq 5$$, add $$1$$ to the thousandths digit, changing $$7$$ to $$8$$.
4. Remove trailing digits: Delete the $$5$$ (all digits to the right of the thousandths place).

The rounded result is $$15.218$$.

Rounding 15.2175 to the Nearest Thousandth

To round $$15.2175$$ to the nearest hundredth, apply the four-step decimal rounding procedure:

1. Locate the hundredths digit: In $$15.2175$$, the digit in the hundredths place is $$1$$.
2. Look at the next digit: The digit immediately to the right of $$1$$ is $$7$$.
3. Compare with $$5$$: Because $$7 \geq 5$$, add $$1$$ to the hundredths digit, changing $$1$$ to $$2$$.
4. Remove trailing digits: Delete the $$7$$ and $$5$$ (all digits to the right of the hundredths place).

The rounded result is $$15.22$$.

Rounding 15.2175 to the Nearest Hundredth

To round $$15.2175$$ to the nearest tenth, apply the four-step decimal rounding procedure:

1. Locate the tenths digit: In $$15.2175$$, the digit in the tenths place is $$2$$.
2. Look at the next digit: The digit immediately to the right of $$2$$ is $$1$$.
3. Compare with $$5$$: Because $$1 < 5$$, leave the tenths digit unchanged at $$2$$.
4. Remove trailing digits: Delete the $$1$$, $$7$$, and $$5$$ (all digits to the right of the tenths place).

The rounded result is $$15.2$$.

Rounding 15.2175 to the Nearest Tenth

You are assisting in the development of a training manual for new account clerks at a financial services firm. One section of the manual must explain the company's standard procedure for rounding decimal figures in client reports to ensure consistency. Write a brief instructional passage that lists and describes the four steps required to round a decimal to a specified place value. In your response, clearly detail how to identify the target digit, the criteria used to decide whether to change that digit, and what specifically happens to any digits located to the right of the target place in the final rounded result.

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